This data sufficiency question presents the following situation: "Cars Y and Z travel side by side at the same rate of speed along parallel roads as shown above. When car Y reaches point P, it forks to the left at angle x°, changes speed, and continues to stay even with car Z as shown by the dotted line. The speed of car Y beyond point P is what percent of the speed of car Z?"

(1) The speed of car Z is 50 miles per hour.
(2) x = 45

The correct answer is B. I don't understand the solution pertaining to the second statement that explains how "(√2dz)/ry = dz/rz" converts into "ry = √2rz" Could you explain this relationship in more detail, please?

Hey atomico,

Perhaps looking at this one from a different perspective would help. We know that:

Rate = Distance/Time

And they're asking us for the relationships between the rates of the two cars. It's then important to know that both cars will reach the same horizontal distance (as denoted by that dotted line) at the same times, so the times in the denominator of each relationship will be the same.

The difference is in the actual distance traveled, and we know that a 45-degree angle gives that distance a relationship of x to x(sqrt 2), based on the 45-45-90 triangle properties. So if the second car travels at a distance of (sqrt2) * Distance of the first car, then our Rate calculations are:

Rate (first) = Distance/Time

Rate (second) = sqrt 2 * Distance / Time

Then we know that the rates have a proportional relationship of x to x(sqrt 2), and we can calculate the percentage difference in their rates. That is why B is correct.